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Physics 2211

Physics 2211. Force and Acceleration with respect to Circular Motion and the Concept of Pseudo Forces . Newton’s Three Laws of Motion.

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Physics 2211

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  1. Physics 2211 Force and Accelerationwithrespectto Circular Motion and the Concept of PseudoForces.

  2. Newton’sThreeLaws of Motion • In ordertoobtain a full grasp of therelationshipthatforce and accelerationhavewith circular motion, Newton’sthreelaws of motionmustdefined. • They are… • A particle in motionor at restwillremain in motionor at restunless a forceisacteduponit. • A particle’saccelerationisdirectlyproportionaltothe net forceactingonit and inverselyproportionaltoit’smass. • Iftwoparticlesinteract, theforce of particleoneonparticletwoisequal and oppositetheforce of particletwoonparticleone.

  3. CircularMotion AccordingtoNewton’sfirstlaw of motion, in a perfectatmospherewherethere are no forces, objects are either at restor at constantvelocity. However, thisisonly true in veryfewcircumstances. Observationrevealsthatacceleration and decelerationoccursallaroundus. ThisbringsustoNewton’ssecondlaw of motion. Newton’ssecondlawsimplystatesthat in orderforobjectsorparticlestoacceleratetheremustbe a forceactingontheseparticles. Thisis true forparticles in circular motion. Theremustbe a forceactingontheseobjectsto cause themtoaccelerate and decelerate. Withthistheory as background, thefirst idea to circular motionisthat in circular motionthereisvelocity and acceleration.

  4. Acceleration and Circular Motion Theacceleration in circular motionisgiven as… a = |v|²/r Where a isacceleration, v isvelocity, and r istheradius of thecircle. As thisequationdepicts, thedirection of acceleration in circular motionisalways in towardsthe center of thecircle because the direction of r is towards the center of the circle. However, it has alreadybeenstatedthattheremust be a forcethatyieldsthisacceleration. Thisforceispresentated as… F = m × a = m × (|v|²/r) Fromthisequation, thedirection of forceisalsotowardsthe center of thecirclewithrespectto circular motion. A goodexamplethatwillsolidifythis concept is a car on a racetrack.

  5. Example: RaceTrack On a racetrack, the cars are racingaround a trackthatis in a circle-circular motion. As the cars are in motion, theacceleration of the cars pullsthem in towardsthe center of the of theracetrack. Considerthepicturebelow…

  6. A BankedRacetrack In thepreviousexample, imagine thattheracetrackwould be banked. Thiswouldhave a noticableeffectonthepull of accelerationtowardsthe center of thecircle. Examine thepicture. Themgsinθisanotherone of theforcesonthe car thatwillpushittowardsthe center of theracetrack. Iftheracetracisbankedenough, the driver can keepthesteeringwillstraight and stillgo in a circlearoundtheracetrack.

  7. Psuedo and FictitiousForces • A fictitious or pseudo force is one that is not real but caused by a force that is real. Usually, it is in the opposite direction of the real force. • Many times a fictitious force is felt because a person is in an accelerating reference frame. • Consider a car decelerating. As the driver applies the brakes, the direction of the actual force is opposite the direction the car would be travelling. However, the driver would experience a force pushing him towards the direction the car is going. This force would be called the pseudo or fictitious force, and the same example would apply for a car accelerating. • Pseudo forces are measurable. • Watch out for pseudo forces.

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